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arXiv · 2508.10662

The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem

Athanasios Christou Micheas
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Abstract

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the definition and properties of a new space of functions, which will be called multivariate Taylor measure function space. The proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases.

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Athanasios Christou Micheas. 2025-08-14. The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem. https://arxiv.org/abs/2508.10662

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